Chelsea were fined £10 million ($13.4 million) in July and given a suspended two-window transfer ban in relation to breaches of Premier League rules during the Roman Abramovich era.
The club had admitted to 74 breaches of FA regulations covering agents, working with intermediaries and third-party investment in players.
Owners Todd Boehly and Clearlake Capital self-reported the breaches to football authorities in 2022, when they were in the process of buying the club from Russian billionaire Abramovich.
The breaches involved deals to take Eden Hazard, Willian, David Luiz and Nemanja Matic to Stamford Bridge, all central to Chelsea's 2016-17 triumph under Antonio Conte.
Pochettino, whose Spurs team finished seven points behind Conte's Chelsea, believes the authorities did not go nearly far enough.
"We should win one Premier League, we should have been awarded it," Pochettino told reporters.
"If that was true, then we deserve to be champions that year, for sure. They were punished, they admitted it? So that’s it. The title should be for the team that was second.
"We can say that they scored goals, they won games. OK. But it's completely fair to say that we didn't compete before the start of the season with the same card.
"Maybe with the same rules, we could've signed some players that would have made the team better or scored more goals."
Pochettino, who currently coaches the USA national team, went on to manage Chelsea in 2023-24.
"'I have no doubt and I'm not scared to say the truth. The Chelsea fans will be upset with me but if we were at Tottenham and broke the rules, I'd admit the same: 'We don't deserve the title because we broke the rules.'
"It's impossible if only some clubs play with offside and another plays with no offside. Or one plays with VAR and another plays with no VAR.
"For everyone it needs to be the same rules. And then you have the capacity to create the best team.
"I don't say that Chelsea didn't play well, that Conte was not great. I don't say that. I don't want the message to be twisted.
"But if you broke the rules then ciao, you need to give it to another team. I don't know why that didn't happen.
"What is being promoted and incentivised is to break the rules."
Pochettino was in charge of the USA during the World Cup and last month signed a contract extension to remain in position until the 2030 World Cup
